The demand function for price increases and for price cuts for an oligopolist ar

Question

The demand function for price increases and for price cuts for an oligopolist are, respectively,

Q1 = 210 - 30P1 or P1 = 7 - Q1/30

Q2 = 90 - 10P2 or P2 = 9 - Q2 /10

The oligopolist's total cost function is: TC = 3.5Q + Q2/60

(a) Derive the MR1, MR2, and MC functions facing the oligopolist.

(b) Determine the price and output at the kink on the demand curve.

(c) Determine the upper and lower limit of the MR gap and prove that MC falls in the MR gap.

(d) Find the value of the total profits of the oligopolist.

Explanation / Answer

(A) Q1 = 210 - 30P1 or P1 = 7 - Q1/30

TR 1 = P1 x Q1 => 7Q1 - Q21/30

MR1 = d TR1 / dQ1 =>  7 - Q1/15

TR 2 = P2 x Q2 => 9Q2 - Q22 /10

MR2 = d TR2 / dQ2 => 9 - Q2 /5

TC = 3.5Q + Q2/60

MC = dTC / dQ =>  3.5 + Q/30

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